1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "ground/relocation/pr_nexts_eq.ma".
16 include "ground/relocation/tr_nexts.ma".
18 (* TOTAL RELOCATION MAPS ****************************************************)
20 (* Constructions with pr_eq and stream_eq ***********************************)
22 corec lemma eq_tr_inj_bi (f1) (f2): f1 ≗ f2 → 𝐭❨f1❩ ≐ 𝐭❨f2❩.
23 * -f1 -f2 #p1 #p2 #f1 #f2 * -p2 #H
25 [ @pr_eq_push /2 width=5 by/
26 | #p @pr_eq_next [3:|*: //]
27 cases tr_inj_fold cases tr_inj_fold
28 /3 width=5 by stream_eq_cons/
32 (* Inversions with pr_eq and stream_eq **************************************)
34 corec lemma eq_inv_tr_inj_bi (f1) (f2): 𝐭❨f1❩ ≐ 𝐭❨f2❩ → f1 ≗ f2.
35 cases f1 -f1 #p1 #f1 cases f2 -f2 #p2 #f2
36 cases tr_inj_unfold cases tr_inj_unfold #H
37 cases (pr_eq_inv_nexts_push_bi … H) -H #H1 #H2
38 @stream_eq_cons /2 width=1 by/